Control of impedance of semiconductor amplifier circuits



L. BARNEY CONTROL OF IMPEDANCE OF SEMICONDUCTOR April 24, Y1951AMPLIFIER CIRCUITS 6 Sheets-Sheet 1 Original Filed Nov. 6 1948 Apri124,1951 H. L`. BARNEY CONTROL 0F IMPEDANCE 0F' SEMICONDUCTOR AMPLIFIERCIRCUITS 6 Sheets-Sheet 2 Original Filed Nov. 6, 1948 TRANS/S TOR E OUIVALL' N T CIRCUIT PARAMETERS so,ooo

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10poble @ILL/Auping) /Nl/ENTOR BV H.L.BARNEV #Welfwf ATTORNEY April 24,1951 2,550,518

H. L. BARNEY CONTROL OF IMPEDANCE 0F SEMICONDUCTOR AMPLIFIER CIRCUITSOriginal Filed Nov. 6. 1948 y 6 Sheets-Sheet 3 @WWU-)Jaff- ATroRA/EVApril 24, 1951 H. L. BARNEY 2,550,518

` CONTROL 0F IMPEDANCE 0F' SEMICONDUCTOR AMPLIFIER CIRCUITS v OriginalFiled Nov, 6, 1948 6 Sheets-Sheet 5 F lG. 2.9

A 7' TORNE V Aprll 24, 1951 H. L. BAFmEYA 2,550,518 u CONTROL 0FIMPEDANCE 0F SEMICONDUCTORv AMPLIFIER CIRCUITS Original Filed Nov. 6,1948 6 Sheets-Sheet 6 ATTORNEY Patented Apr. 24, 1951 CONTROL oFIMEpANcE or SEMI-CON- DUo'roR AMPLrFIER OIROUITS Haro-1d L. Barney,Madison, N. J., assigner tonen Telephone Laboratories,

Incorporated, New

York, N. Y., a corporation of New York Original application November 6,1948, Serial No. 58,684. Divided and thisapplication November 15, 1949,Serial No. 127,439

' 11 Claims.

.This application is a division of application Serial No. 58,634, filedNovember 6, 1948. V.

This invention relates to signal translation networks utilizingsemiconductor amplifiers as active elements.

The principal object of the invention is to adjust the impedance of sucha network, viewed at its input terminals or its outputterminals, to adesired value.

More particular objects are: to match the input impedance of such avnetwork to that oi a specified source; to match the Output impedance ofsuch a network to that of a specied'load; to make the input -impedanceofl such a network substantially innite; to make the input or outputimpedance of such a network substantially zero; to make the input andoutput impedances of such a network substantially alike in magnitude.

Related objects are to minimize `or eliminate interstage couplingdevices from translating ap p aratus of a plurality of stages, each ofwhich comprises a semiconductor amplifier network, and to match theimpedance of such apparatus as a whole to that of va specified sourceand its out'- put impedance to that of a specified load.

Application SerialNo. 11,165' oi John Bardeen and W. I-I. Brattain,iiled February 26, 1948, and now abandoned describes and claims anampli- Iier unit of novel construction comprising a small block ofsemiconductor material, such as N-type germanium, with which areassociated three electrodes. One of these, known as the base electrode,makes low resistance contact with a face of the block. It may be aplated metal nlm. The

others, termed emitter and collector, respectively, :n

preferably make rectifier contact with the block. They may, in fact, bepoint contacts.v The emitter is biased -to conduct inthe forwarddirection and the collector is biased to conduct in the reversedirection. Forward and reverse are here used in the sense in which theyare understood in the rec tier art. When a signal source is connectedbetween the emitter and the base and a load is con- 2 Jr., Serial No.45,023, filed August 19, 1948..- ,The device in'all of its forms hasreceived the appellation transistor, and will beso designated in thepresent specification. i

Infthe original Bardeen-Brattain application above referred to, `thereappears a'."tabulationl of the performance characteristics o threesample transistors. crernents of signal current which iiow in thecircuitof the collector electrode as a result of the signal current incrementswhich flow in thecircuit of the emitter electrode exceed the latter inmagnitude. This feature of transistors has become the general rule, andappears in nearly all transistors fabricated. It is discussed in detailin an application of John Bardeen and W. H. Brattain, Serial No. 33,466,i'lled June 1'7, 1948, issued October 3, 195,0, as Patent 2,524,035vwhich is a continuation in part of the earlier application of the sameinventors. It is of such importance .in connection with the presentinvention, as well as otherwise, that the ratio ofy these increments hasbeen given aname, a In Oneof4 its aspects, although not exclusively, thepresent invention dealswith transistors in which a 1 ('a exceeds unity)and is based on the discovery that with a network of which such a deviceis the active element, the impedance looking into its input or outputterminals can, by appropriate proportioning of one of the networkparameters in re lation to the transistor parameters, be made to vtakeon Values which vary overla much wider range than is possible with themost nearly analogous Vacuum tube networks. `It will be exlplainedbelow, in the detailed description of the invention which follows, howit is that. the Value of a resistor included in the one circuit modiesthe vimpedance of the other circuit.

fffihe inventionvwill be fully apprehended from the following detaileddescription of certain preferred embodiments thereof, taken inconnection with the appended drawings, in which:

Fig. l is a schematic diagram of a transistor;

. Fig. 2 is a symbolic representation of a transistor as employed in thepresent specification;

Fig. 3 is a schematic circuit diagram of a transistor amplifier networkof the grounded base type.; l

Eig. 4 is the equivalent circuit of a transistor;

Fig. 5 is the equivalent circuit of the transistor network of Fig. 3;

Fig. 6 is a group of graphs showing transistor parameter values asfunctions of emitter bias current;

Figs. 7, 9 and ll are graphs showing the varia- In one of these, itappears that intion of the input impedance of the network of Fig. 3 withload resistance for three representative types of transistorcharacteristic;

Figs. 8, 10 and 12 are graphs showing the variation of the outputimpedance of the network of Fig. 3 with source resistance under the sameconditions;

Fig. 13 is a schematic circuit diagram of a transistor amplifier networkof the grounded emitter type;

Fig. 14 is the equivalent circuit of Fig. 13;

Figs. 15, 17 and 19 are graphs showing the variation of the inputimpedance of the network of Fig. 13 with load resistance for threerepresentative types of transistor characteristic;

Figs. 16, 18 and 20 are graphs showing the variations of the outputimpedance of the network of Fig. 13 with source resistance under thesame conditions;

, Fig. 21 is a schematic circuit diagram of a transistor amplifiernetwork of the grounded col- .lector type;

Fig. 22 is the equivalent circuit of Fig. 2 1;

Figs. 23, 25 and 27 are graphs showing the v,variation of the inputimpedance of the network fof Fig. 21 with load resistance for threerepresentation types of transistor characteristic;

Figs. 24, 26 and 28 are graphs showing the= tively;

Fig. 37 is a schematic circuit diagram of an amplifier comprising aplurality of similar transistor amplifier stagesin tandem;

Fig. 38 is a Schematic diagram showing a twostage amplifier of which theindividual stages are unlike;

Figs. 39, 40 and 41 are schematic circuit diagrams of modications of theamplifier of Fig. 38.

In Fig.'1 there is shown a diagrammatic representation of a transistorcomprising a block l of Asemiconductor material, having a plated film 2of metal making low resistance contact with one face, an emitterelectrode 3 and a collector electroded, `making contact close togetheron the opposite face. A base electrode is connected to the film 2. Tosimplify the drawings, a symbolic representation, shown in Fig. 2, isused henceforth. In this gure, the emitter 3 is distinguishedbyanarrowhead which points inward for N-type material, the collector 4 bymaking contact on the same face of the .block as the emitter, and thebase electrode 5 by makingr contact on the opposite face. The shortheavy line 6 represents the block itself. v

Fig. 3 is a schematic circuit diagram of a transistor amplifier networkin which the transistor itself is represented by the symbol of Fig. 2. Abias source Ill of perhaps 4.0 volts is connected to apply -negativebias potential to the collector 4, while another source il, usually of afraction of a volt, is connected to apply a small positive biaspotential to the emitter 3 (or a small negative v bias potential to thebase electrode 5, depending upon ones point of View). A load representedby an impedance Z2, which may be variable, is connected in the collectorcircuit. A signal source I2 is connected in the input circuit, i. e.,between the emitter 3 and the base 5. In addition, an external or sourceimpedance Z1 is connected in the input circuit. This impedance evidentlyreduces the signal voltage applied to the input terminals of thetransistor, for a given source voltage, but it serves an importantpurpose as will more fully appear below.

As is now well known, the voltage which appears across the loadimpedance Z2 contains a component which is an amplified replica of thesource Voltage. In addition, it is found that in the great majority oftransistors, a is so great that the signal frequency component of thecollector current exceeds the signal frequency component ofthe emittercurrent even when the network load impedance Z2 is of substantialmagnitude.

The collector signal current ic, corresponding to a given emitter signalcurrent ie, depends on the collector voltage and on the circuitconfiguration. Therefore a cannot be exactly specified withoutspecifying these matters. A suiiiciently exact deiinition of a istherefore 1:(22) V const. grounded base connection (l) or, a is equal tothe ratio of collector signal current to emitter signal current when thebase electrode 5 is common to the input and output circuits and when thecollector voltage is held constant. In a network of this coniigurationin which a constant potential source supplies operating bias to thecollector and in which signal frequency collector currents iiow througha load impedance Z2 and cause signal frequency changes in the collectorvoltage, an equivalent deiinition of a, namely,

i a Lim i Zz-o ze Such an equivalent circuit is shown in Fig. 4. Theseelements of the equivalent circuit are identified herein as emitter,collector and base impedances, but it is to be understood that an actualimpedance measurement between two electrodes of the transistor would notnecessarily give the simple sum of the respective two impedances. Thevalues of the equivalent circuit elements may be arrived at from suchexternal impedance measurements as follows:

where Zu is the impedance measured between the emitter and the baselwith the collector circuit eiectively open;

current flowing in the emitter circuit when the collector circuit iseffectively open.

The assumed directions of current IioW and the polarity of theelectromotive force of the internal generator I3 are as shown in Fig. 4for the above measurements.

Fig. 5 is an equivalent circuit corresponding to the transistoramplifier network of Fig. 3, which is of the grounded base type; i. e.,the base impedance Zt is common to both meshes, while y the emitterimpedance Ze and the collector impedance ZC are individual tothe iirstand second meshes, which are identified by mesh currents i1 and i2 inthe customary manner. Test vol-tage sources e1 and c2 are connected inthe first and l second meshes for purposes of analysis.

As ywith Fig. 4, there appears in series with the collector impedance asource -of electromotive force CIzmic (3) As above stated., thefictitious electromotive force e `which is characteristic of thetransistor is found to be substantially proportional to the emittercurrent ie. The constant of proportionality thus has the dimensions ofimpedance, is termed a mutual impedance, and is designated Zm.

It is of interest to determine the relation which must hold in orderthat The foregoing definition (2)4 of a requires that it be determinedwhen the output terminals of the transistor network are short-circuitedfor signal frequency currents. present purposes, the source can betreated as having no internal resistance. Thus, putting and solving theEquations 5 and 6 simultaneously kfor i1 and i2 gives Zb+ Za T (s) whereA is the determinant of the coefficients of Equations 5 and 6. But inFig. 5,

and therefore 'Le Z1 Tests of a large number of sample transistors haveshown that the various impedances of the equivalent circuit areessentially pure .resistances Furthermore, yfor the except at very highfrequencies andthat, within this resistive range, representative valuesare:

Thus both Zm and Z0 are many times as great as Zb; so that, fromEquation 10, to a good approximation,

Z7" a Y ZE Though the expressions developed hereinafter for input andoutput impedances are general, the results which follow will beillustrated with examples involving resistive terminations, and for thatpart of the frequency scale in which the transistor equivalent circuitparameters are resistive. These parameters, when used in thisconnection, will be referred to as re, rb, rc and rm instead of Ze, Zt,Zc and Zm, respectively. Y Out of the Iwide range of possiblecharacteristics available among transistors, the results will beillustrated withthree different sets of equivaient circuit parameters.The first, which will arbitrarily be referred to as type 1, satisfiesthe following conditions a 1 and To illustrate this type, the followingequivalent circuit parameter values are assumed:

re=500 ohms rb=100 ohms re=20,000 ohms 1an-:10,000 ohms Type 2characteristics are obtained when the following conditions are met:

a 1 and Values of equivalent circuit parameters assumed to illustratethis type are:

re=500 ohms rb=100 ohms rc=20,000 ohms T1n:40,000 Ohms Type 3characteristics are obtained when a 1 and To illustrate this type, thefollowing values are assumed:

re=500 ohms M2600 ohms r=20,000 ohms rm=40,000 ohms (Ie). At theoperating point of 0.5 milliampere emitter current, it will be seen thatbut allowing Z1 and e2 to remain finite, it turns out that I These moregeneral Equations 14 and 15 may be replaced by the following equationsfor illustrative purposes:

assuming Z1 and Z2 to be replaced by R1 and R2.

In transistors of type 1, a l, so that Tm r, and both of theseexpressions give positive values for all positive values of R1 and R2.The variation of Rin and Reut with R2 and R1, respectively, is small.

The variations of R111 and Rm are plotted in Figs. l

'7 and 8 as functions of R2 and R1, respectively, for the type 1transistor whose parameters were given above. The input resistance, asshown in Fig. 7, varies between 550 and 600 ohms for a variation of Rebetween zero and iniinity and the output resistance, as shown in Fig. 8,varies between 13,400 and 20,100 ohms or a variation of R1 between zeroand innity.

In transistors of type 2, a 1 but l f, f.+r.+;% 16) The variations ofR111 and Reut with R1 and R2 as shown on Figs. 9 and 10 for a transistorof this type are somewhat greater, but both are still positive for al1positive values of R1 and R2.

With the type 3 transistor parameters, where startling new results areobtained. These are revealed in Figs. 11 and 12, which are plots ofinput resistance as a function of R2 and of output resistance as afunction or R1. it is apparent that both the input resistance andtheoutput values of R2 and R1, respectively, and are positive for greatervalues and negative for smaller. Thus there is furnished a transistornetwork capable of giving amplification, and which has Zero or negativeinput resistance or zero or negative output resistance. Furthermore,these results are independent of one another, so that they may beobtained separately or together, as desired, within the limitationsimposed by stability requirements. it will be evident from inspection ofFigs. 11 and 12, that this arrangement is not short-circuit stable. Thatis, if both R1 and R2 are zero, the network may break into oscillationbecause of the negative resistances of the input and output circuits. IfR120, R2 must be at least 1550 ohms, or if 232:0, R1 must be at least82.5 ohms to obtain a stable arrangement.

The critical value of R2, for which Rm=0, is given by mmf-re) R2- Trl-TbSimilarly, the output resistance Reut is zero for mm1-n) A Rl- Tc+TbTransistor networks of the type shown in Fig. 3, in which the input oroutput resistance has been adjusted in the manner described above tohave a Zero value, are of use in current measuring instruments. Those inwhich the resistance has been adjusted to a negative value are of use asnegative resistance boosters, and the like. On the other hand, andespecially when a 1, the in- Vention provides a simple and convenientadjustment of the magnitudes of the input and output impedances of suchnetworks to match positive source and load impedances, respectively.

Fig. 13 shows a transistor connected into a net- .Work of the so-calledgrounded emitter type.

As shown by the equivalent circuit, Fig. 14, this term means merely thatthe emitter impedance Z0 is common to the two meshes while the baseimpedance Zb and the collector impedance Ze are u individual to theseparate meshes. The fictitious electromotive force e which ischaracteristic of the transistor is again given by but the emittercurrent is is now replaced by the .diierence between the mesh currentsi1 and iz. Thus Ze='L2-L1 As before, a test voltage source c1 and aninput impedance Z1 are connected to the input terminals while a secondtest voltage source e2 and a load impedance Z2 are connected to theoutput terminals. Mesh equation analysis of the circuit of Fig. 14 inthe manner outlined above gives These may also be rewritten forfrequency ranges which are not too high, as

where Z1 and Z2 are replaced by R1 and R2. These latter expressions areplotted as functions of R2 and Ri, respectively:

(a) In'Figs. 15 and 16 for the illustrative parameter values previouslychosen for type 1 transistors, with which a 1 and o in Figs; 17 -and' isfor the illustrative parameter values previously chosen for type 2transistors with which a 1 and (c)v In Figs. 19 and 20 for theillustrative parameter values previously chosenV for type 3 transistorswith which a 1 and With the type 1 transistor characteristic in which 1,the input and output resistances re- 'main positive for all values of R2and R1, respectively, though their magnitudesare controllable byadjustment of these resistors.

But when a 1, startling results occur. Thus, in Figs. 17 and 19, theinput resistance becomes infinite for a load resistance given byR2=rm-rerb (22) being positive for greater values and negative forlesser values. In addition, and subject to the con- The proximity, alongthe Rzaxis, of the points for which Rinzl and Rm= o makes it a simplematter to vary R2 between these values in any desired manner, and soadapts `the'network of Fig. 1-3, when incorporating atransistorof type3,

`to use in modulation systems of the so-called absorption modulationtype. Referring to Fig. 18,

' rthe output resistance for the network with a type 2 transistor iszero at a value of Ri which, from Equation 21a is given by beingpositive for lesser values and negative for greater. For a type 3transistor,for which rm n+rclLTc the output impedance is alwaysnegative, but is `:variable over a wide range of adjustment of R1.

The network of Fig. 13, when adjusted in the Y* manner described above,in addition to providing amplification, is useful for matchingimpedance, as a negative resistance, as a Zero impedance device, and invarious other connections.

Fig. 21 shows a transistor connected in a network of the so-calledgrounded collector type. As shown by the equivalent circuit, Fig. 22,this `term means merely that the collector impedance Y Zs is common tothe two meshes while the base impedance Zb and the emitter limpedance Zeare individual to the separate meshes. The fictitious .electrornotiveforce e' which characterizes the transistor performance is againconnected in series with Ze and is given by e=Zmie but in this caseie=i2 l i Test voltage sources e1 and ez and source and `load impedancesZ1 and Z2 are connected between the input terminals and between theoutput terminals, as before. Mesh equation analysis of the circuit ofFig. 20 in the manner outlined above gives Considering the less generalcase of purely resistive elements, we have on rewriting:

Mrd-r2) Rin`=1`b+T4- Q+TC I RZ TM (25a) (R1+Tb (r-Tm) I Rank-7.24"Tc+Tb+Rl I when R1 and R2 are substituted for Z1 Vand Z2, respectively.These resistances are plotted',l as

functions of R2 and R1, respectively, l (a) In Figs. 23 and 24 for atransistor of type .1,

It will be noted that the curves of these figures are the same in manyparticulars as those of Figs. 15 to 20. Thus, the conditions under whichRin reaches infinity in Figs. 25 and 27 are identical with those forwhich the same result arises in Figs. 17 and 19. Again, the conditionsfor which Rbut reaches zero in Fig. 26 are the same as those for whichthe like result occurs in Fig. 18. The particular values of R2 and R1which Which isidentical with the value of Ri for which Roni reaches zeroin Fig. 18. The value of R2 for which Rin has a zero value, in the oaseof vtransistors of type 3, is

Tbm-Tc) ,R2- rb-I-ra Thenetwork of Fig. 21, when adjusted in` lthemanner described above, can be put to use in any v30 shows theequivalent circuit. Fig. 22 by the addition of the padding resistor Rpin series with the collector.

rvzatte-,51e

. li of the various connections above referred to in connection with theVother figures.

It will be `observed that in Figs. 19 and 27, those regions areindicated as being unstable in which the input impedance is positive forvalues of the load resistance less than that for which it isnegative. Tounderstand the nature and explanation of this instability, consider rstthe plot of the output impedance as a function of source resistance,Fig. 2i). This is a negative resistance for any and all values of sourceresistance between zero and infinity. This negative resistance is of theso-called series-type, i. e., the network of Vwhich it forms a part willbe stable only ii atpositive resistance is connected in series with it,of which the value is greater than that ofthe negative resistance. Byway of lexample, assume that the source resistance Ri is zero. From Fig.20, the output impedance then 'appears-"asa negative-resistance of -1550ohms. If a load resistance R2 equal to or greater than 1550 ohms isconnected to the output terminals Vof the transistor network, thenetwerk as a whole will be stable. Ii, however, the value of theexternal load resistance is less than 1550 ohms, the net resistance inthe output circuit will be negative and the'networkV will oscillate orsing. Addition of resistance Ri in the input circuit does not. cure thesituation but only makes things fthe negative output resistance for Zeroinput resista'nce, the system as a whole Will be inherently unstable,even though its input impedance appears to be positive, as indicated inthose parts of Fig. 19 which lie in the shaded area.

The explanation 'of instability in the case of Fig. 27. is the same asthat of Fig. 19 except for 'ruimerieal values.

With the networks described above, it is possible to design a singleamplifier stage whose input impedance or output impedance isrespectively matched te the impedance of a source or of a load as longas these are not too high or too low. l V1li/'further problem ariseswhen one of them y'IS innite ory Zero.

l u Take, for example, the conimon situation in which it is desired thatthe input impedance of an amplier be substantially infinite whilev itsoutput impedance has a speciff'ied' value between zero and innity. Thisprobler-1i' may be illustrated in connection with Fig. 2l.

The'input impedance may be made infinite by so'` lthciosiiig R2 that thedenominator of (25) vanishes; but it may happen that the load with whichthe network is to work has a resistance of vwidely diierent value.

This problem is solved, in accordance withthe invention in one of itsaspects, by the use of an additional variable parameter in the form of apadding resistor.

IIt may be readily appreciated that the addition of a resistance inseries with emitter, base, or collector is equivalent in effect toincreasing the magnitude of re, rs or rc respectively, in the foregoingequations for input and output resistance. Fig. 29 illustrates theprinciplegas applied to the grounded collector neiwvork of Fig. 2l, andFig. It differs from Solution of the neti 2 work equations in the mannerheretofore described but for resistances directly, instead of for themore general impedances yields, for the input resistance:

Tb-I-rc-l-Ri-I-Rp It is evident from these equations that the loadresistance R2 may be independently chosen, and that it is still possibleto make the input impedance innite by adjusting the sum of R2 and thepadding resistor Rp, while using a value of the load resistance R2 whichmay be dictated by other consideration l With the network of Fig. 29, afraction of the power output of the transistor is absorbed in thepadding resistor and is therefore not available to the load. Under somecircumstances this may be objectionable; and to reduce this power losswithout sacricing the impedance matching advantages of Fig. 29, resortmay be had to still another transistor network which is illustrated inFig. 3l, while its equivalent circuit is shown in Fig. 32. This networkis the saine as that of Fig. 21 except for the addition of a feedbackresistor RF in shuntwith the transistor and its load R2. This additionresults in the addition of a third mesh to the network, designated is inFig. 32. Solution of the mesh equations yields, for the inputresistance:

From Equation 31 it is evident that, within the restriction T'ln(R2I-'l`e+c) the input impedance may take on values which are positive,negative, zero, or infinite, as required, in dependence on the Values ofR2 and Rr. This evidently gives greater freedom in the selection oi theload resistance, as compared with Equation 25 which applies to thenetwork of Fig. 2l, in the same manner that the use of the paddingresistor in Fig. 3l provides suoli freedom. At the same time, all of thepower output of the transistor is furnished to the load, at the expenseof some power absorbed in RF. The latter power is driven from the sourcerather than from transistor. This difference is of advantage under somecircumstances.

' In the vacuum tube amplier art, it is known that certain advantagesaccrue from the use of Vnegative or inverse feedback. The conventionalcathode follower vacuum tube circuit with large, unbypassed cathoderesistor embodies the inverse feedback principle, and, as is well known,the input impedance of such a circuit, lc-cking into its grid and loadresistor terminals is greatly increased, as compared with that of agrounded cathode circuit employing the same tube. The networks of Figs.21, '29 and 3l may be looked upon as embodying the same negativefeedback principle but they differ from the most Vnearly analogousvacuum tube circuits in that 13 the input impedance may take on thewidely varying values discussed above. The eifect of the resistor Re inFig. 31 may be locked upon as further increasing the inverse Vfeedbackof Fig. 21 by providing a second path, in addition to that through thesource resistance R1, through which the feedback current can now, and sofurnishing a greater current to the base electrode for a given voltagedrop across the load resistor, or a lgreater voltage feedback fora givenemitter current, depending on .ones point of view. The mode of operationof the network of Fig. 31 can also be looked upon as follows:Elimination of the padding resistor RP of Fig. 29 effectively reducesthe total resistance in the output circuit of the transistor below theValue at which the input impedance becomes infinite. As a result, theinput impedance of the transistor, without the feedback resistor yRr, isnegative. Insertion of the feedback resistor RF of the proper magnitudenow places a positive resistance in shunt with the negative inputresistance of the transistor network of just such a magnitude as tobring the input impedance of the network asv a whole back to infinity.

Still further flexibility results when the padding resistor Rp of Fig.29 and the feedback resistor RIF of Fig. 3l are embodied in the sametransistor network. Such a network is shown in Fig. 33 and itsequivalent circuit is shown in Fig. 34. lThe expressions for the inputand output impedances are like those for Fig. 31 but for the fact thatthe collector resistance re' is toA be replaced, wherever it occurs, by

Tc|Rp and that the condition (32) is replaced by Tm (Rz-l-Te--Tc-i-Rp)(33) Instead of merely increasing the inverse feedback due to Re by theuse of a shunting resistor as inFig. 33, an additional negative feedbackcurrent may be drawn from the collector and fed `to the base electrodeby way of a feedback resistor RF, as in Fig. 35. Here C1 and C2 aremerely blocking condensers of negligible impedance at signal frequenciesand are omitted from the equivalent circuit Fig. 36. The resistor RFtherefore carries a current to th-e base electrode, which current is inphase with the collector voltage. In the absence of the feedback path,there is a phase reversal between the voltage on the base electrode andthe voltage onfthe .differences, though slight from the analyticalstandpoint, may become critical in particular circumstances.

The various networks of the invention may be coupled together in variousways; Fig. 37 shows a three-stage amplifier coupling an in coming line2D to an outgoing line 2l. Characn teristic impedances of these linesmay be alike. The operation of tandem stages without using interstagetransformers presents a problem to the designer of transistor networkswho has notthe lcenet of the present invention. The input`resistarlce'of the first stage may be matched to the resistance of thesource, that is of the incoming line 2B, by use of the appropriatetransforma'- tion ratio in an input transformer 22. In each stage theresistances R3 and R4 may be assumed to be very high resistances so thatthey do not appreciably shunt the output of the stage ahead of it or theinput of the following stage. i The load on the first stage is thereforethei series combination' of an` interstage resistor Rs' and the inputimpedance of the second stage. Since Rs appears both inthe inputimpedance and the output'impedance, it may be adjusted to serve bothpurposes.

The application of the foregoing principles to this particular problemis illustrated for a typical transistor of type 2, in which rb= ohmsre=500 ohms rer-20,000 ohms rm=40,000 ohms The output load on the rststage is the sum of Rs and the input impedance of the following stage.Equation 20a is a general expression for the input resistance of agroundedl emitter transistor amplifier stage as a function of its loadresistance. In this expression, replacing'I-ba by Rs+Rm givesacwrRsJfRin) Tc+Tc+RS+Rin-Tm Insertion of the numerical values listedabove in this expression gives ohms Inserting the foregoing numericalvalues, with Rm still undetermined, gives (5w-40,000) (Rin-l- 100)Rift-1004600 The conditions of the problem are that the inputterminating resistance of each stage shall be equal to the seriescombination of Rs with the output impedance of the prior stage, or

Simultaneous solution of these three equations gives, for the assumednumerical values:

Since the stages are all to be alike, this result holds for any stage,so that a multistage ampliner of as many stages as may be desired can bebuilt up, in which all input and output impedances are 4,500 ohms, andin which, furthermore. the effective output impedance of the last stage(Ruim-Rs) is likewise 4,500 ohms. Transformers 22, 23, or otherimpedance matching networks may now be connected at the inputand'ou'tput 'terminals of the amplifier asa whole to effect-a match tothe incoming and outgoing lines 20, 2l. Each stage of the amplier, usingthe assumed numerical values, has a power gain of 18 decibels, whichwould be impossible to secure in a multistage amplier in whichinterstage impedance matching was obtained, merely by the use of paddingresistorslin series with the input circuits and potentiometers in theoutput circuits.

1 It Willbe noted that, in Fig. 37,the emitter bias battery H oftheearlier' gures has been omitted.

It is replaced, in the iirst stage, by a self-bias circuit of the typewhich forms the subjectmatter of an application of R. C. Mathes and H.L. Barney, Serial No. 22.854, filed April 23, 1948-and issued August 8,1950, as Patent 2,517,- 960 and in the second and third stages by adifferent self-bias arrangement, which forms the subject-matter of anapplication of H. L. Barney, Serial No. 123,507, filed October 25, 1949.The shunt resistors R4 are required to be of fairly low value from thestandpoint of self-bias alone While, in order to reduce their shuntingeffect across the input terminals of the amplier stage, they arerequired to be of high value. These incompatible requirements canberesolved by the addition of a v tial drop which is nearly equal inmagnitude to y that across the shunt resistor R4. By this meansself-bias of the base electrode with respect to the emitter in therequired magnitude of a fraction of a volt is secured for thetransistors of the second and third stages Without resortY toaninterstage transformer.

Under some circumstances the restrictions placed on the amplifier ofFig. 3'7 may be considered too severe. For most purposes a suincientrequirement is that (a) the input impedance of the first stage of anamplifier match the source impedance; (b) the output impedance of eachI-stage match the input impedance of the following stage; and (c) vtheoutput impedance ofthe last kstage match the impedance of Athe load.Requirements of this type may be met comparatively simply in a two-stageamplier network with arcircuit suchas that of Fig. 38, in whichtransistors having type 1 characteristics areused. Here, assumingv thevalues lof resistors Rs and Re, which merely .supply operatingpotentialsto the electrodes, to be high, the load on the rst or grounded-emitterstage consists merely of the input impedance of the second stage. Thus-condition (a) may be met by selecting the first stage outputtermination in accordance with Equation 20a; condition (b) is met-byselecting the second stage output termination'in accordance withEquation 25a at-such a value that its input impedance is equal to .theoutput impedance of the first stage as just determined, and, lastly,condition (c) is met by constructingthe resulting output terminationof-.ltwo parts, the load itself and an adjustment'resistorfRs. Thelatter is shown in shuntwith `the load. Circumstances -mayrequire thati-t be-connected in series with.

the load instead;

Fig. 39 shows a .two-stage amplifier of which the nrst stage isrof thegrounded base type (Fig,

3) vwhile the second stage isof thev emitter-fol-yare-self-biasresistors, merely serve to apply cor- )i5 rect operatingpotentials to the electrodes. With the compensating resistors R7 and R7in the circuit, R5 and Re may be of such-large value as not seriously toshunt the source or the rst stage output. By reason of the directinterstage coupling (C1 and C2 are merely blocking condensers) theoutput terminating impedance seen by the first stage is the inputimpedance of the second. In the manner explained above, but using theimpedance expressions appropriate to the networks, namely, Equations 14and 15 for the first stage and 29 and 30 fonthe second, and nallyselecting the adjustment resistor R1 so that when it is connected inparallel With the load as shown, or in series with the load, thiscombination of resistor R1 and the load presents the necessary impedanceto the output terminals of the second stage.

In place of the padding resistor Rp of Fig. 39, the feedback resistor Rrof Figs. 33 and 35 may be employed, if desired, to give flexibility tothe choices of the other resistors. Fig. 40 shows -a two-stage amplifierin which the second stage is like Fig. S1, and Fig. 4l shows one inwhich the second stage is like that of Fig. 35. The impedance matchingprinciples, and the manner in which they are to be put in practice, areas explained above, due regard being had to the expressions governingthe input and output impedances of the transistor network employed ineach case.

In addition to the aforementioned application Serial No. 58,684, filedNovember 6, 1948, reference is made to another divisional application,Serial No. 127,440, filed November 15, 1949, now Patent No. 2,541,322,issued February 13, 1951, and to a related original application, SerialNo. 58,685, filed November 6, 1948.

What is claimed is:

1. An amplier network having an adjustable input impedance whichcomprises a transistor comprising a semiconductive body, a baseelectrode, an emitterV electrode and a collector electrode cooperativelyassociated therewith, said transistor being characterized by a ratio ofshortcircuit coliector current increments to emitter curr-ent incrementswhich, under proper conditions of electrode bias is greater than unity,means including an energy source for establishing said proper biasconditions, an input circuit interconnecting said base electrode andsaid emitter electrode, an output circuit interconnecting said baseelectrode and said collector electrode, and a load resistor Re connectedin said output circuit, said resistor being proportioned in accordancewith the formula RinzrthmLRz-HJ where re=emitter resistance of thetransistor rb=base resistance of the transistor re=collector resistanceof the transistor rm=mutual resistance of the transistor Rin=inputresistance of the transistor network to cause the input impedance of thenetwork to have a desired value.

2. An amplifier network having an adjustable output impedance whichcomp-rises a transistor comprising a semiconductive body, a baseelectrode, an emitter electrode and a collector electrode cooperativelyassociated therewith, said transistor being characterized by a ratio ofshortcircuit collector current increments to emitter current incrementswhich, under proper conditions of electrode bias is greaterthan unity,means including an energy source for yestablishing said proper biasconditions, an input circuit interconnecting said base electrode landsaid emitter electrode, an output circuit interconnecting saidbaseelectrode and saidy collector electrode, and a terminating resistor R1connected in said input circuit, said resistor being proportioned inaccordance with the formula re=emitter resistance of the transistorrb=base resistance of the transistor rc=collector resistance of thetransistor rm=mutua1 resistance of the transistor Rouc=output resistanceofthe transistor network to cause the output'impedance 'ofA the networkto have a desired value. i

3.-An amplier network having .a'substantially Zero, input impedancewhich comprises a transistor comprising a semifconductive body, a baseelectrode, an emitter electrode and a collector electrode cooperativelyassociated therewith, said transistor being characterized by a ratio ofshort-circuit collector current to emitter current which, under properconditions of electrode bias is greater than unity, means including anenergy source 'for establishing said aproper bias conditions, an inputcircuit interconnecting 4said base electrode and said emitter electrode,an output circuit interconnecting one of said two lastnamed electrodeswith said collector electrode, -f

'and a load resistor R2 connected in'said output circuit, said resistorhaving a value given substantially by the formula re=emitter resistance'ofthe transistor rb=base resistance of the transistor rc=collectorresistance of the transistor rm=mutual resistance of the transistor 4.An amplifier having a `substantially zero output impedance whichcomprises a transistor comprising a semiconductve body, a baseelectrode, an emitter electrode and a collector electrode cooperativelyassociated therewith, said transistor being characterized by a ratio ofshortcircuit collector current to emitter current which, under properconditions of electrode bias is greater than unity, means including anenergy source` for establishing said proper bias'conditions, an inputcircuit interconnectingsaidbase electrode and said emitter electrode, anoutput circuit interconnecting said base electrodewith said coliector.electrode, and a terminating resistor R1 connected in said inputcircuit, said resister having a value given substantially by theform-ula Where 5..An amplifier adapted to be connected in cascadebetween a low impedance source land a low impedance load, whichcomprises a iirst 'transistor `amplifier network of the groundedbaseconfiguration, having input terminals, output" terminals; anintrinsically low input impedance and an intrinsically high outputimpedance, a second transistor amplifier network of thegrounded-collector conguration having input terminals connected to theoutput terminals of the first network and an output circ-uit, aresistor, said resistor and said low impedance load being connected insaid circuit, said resistor being proporticnecl, in dependence on thetransistor parameters and on the impedanceof said load, to make theinput impedance of the groundedcollector stage equal to the outputimpedance of the grounded-base stage.

l :6; An amfplier of two stages adapted to be connected between a lowimpedance source and a low impedance load, the rst stage comprising atransistor 'amplifier network of the groundedbase` configuration havinginput terminals, output terminals, an intrinsically low but controllableinput impedance and an intrinsicallyhigh but controllable outputimpedance, the ysecond stage comprising `a transistor network of thegrounded-collector configuration 4having input terminals, outputterminals, an intrinsically high but controllable input impedance and anintrinsically low but controllable output impedance, the input terminalsofthe second stage being directly connected, for signal frequencies,tothe output terminals of the first stage, the input impedance of thesecond stage thus constituting the output termination of the rst stage,a resistor, said resistor and said load being connected to the outputterminals of the second stage, said resistor and said load, takentogether, being soproporticned in relation to the transistor parametersas to make the input impedance of the second stage, and thus the outputtermination-of the rst stagejmatch the output impedance of the iirststage and of such a Value as togrnake the input impedance of the rststagevmatch the im.- pedance'oi the source, said vresistor being soproportioned in relation to said load as to make said resistor and load,taken together, match the output impedance of the second stage.

7. In combination with apparatusesv defined in claim G, an additionalresistor-connected incircuit with the collector electrode of the secondstage, proportioned to increase the eiective value of the second stagecollector resistance in relation to which the first resistor is in partproportioned.

8. In combination with apparatus as dened in ciaim 6, a feedbackresistor connected, for signal frequencies, in shunt with the inputterminals of the second stage network and proportioned to eiectivelyreduce the input terminating impedance of the second stage for whichdesired values of its input and output impedance obtain.

9. In combination with a low impedance source and a transistor amplifiernetwork of the grounded-base conguration as defined in claim 1 havinginput terminals connected to said source and output terminals, andwherein the input impedance Rm oi said network is matched to that of thesource by proportionmentof a loading resistance R, a second transistoramplier network of the lgrounded-collectorj, configuration having input'terminals and output.,terminals, said last-named input terminals being?connected to the output terminals of the rst network, a resistor and alow impedance load connected to the output terminals of the secondnetwork, the input impedance of the second network constituting aloading resistance R2 for the rst network, and being made equal theretoby proportionrnent of said resistor.

l0. In combination with alow impedance source and a iow impedance load,a two-stage ampiiler adapted to be connected in cascade between saidsource and said load which comprises a rst transistor amplifier stage ofthe groundedbase configuration as dened in claim 1 having anintrinsically low input impedance Rml and an intrinsically high outputimpedance, wherein the input impedance Rinl of said stage is matched tothat of the source by proportionment of the rst stage loading resistanceR21 and having output terminals, and a second transistor amplifier stageof the grounded-collector configuration having Aan intrinsically highinput impedance Rin2 and anintrinsically low output impedance, thetransistor of said second stage being characterized by a ratio ofshort-circuit collector current increments to emitter current incrementswhich ex ceecis unity, an input circuit interconnecting the 'baseelectrode of the second stage transistor with its` collector electrodeand connected to the first stage output terminals, an output circuitinterconnecting the emitter electrode of the second stage transistorwith its collector electrode, said low-impedance load and a loadingresistor R22 being connected in said output circuit, said loadingresistor being proportioned in accordance with theformula wherere2=ernitter resistance of the second stage transistor tgzbaseresistance of the second stage transistor rrcg=co11ector resistance ofthe second Stage transistor rmgzmutual resistance of the second stagetransistor Rm2=input resistance of the second transistor stage,

whereby the second stage input impedance is matched with the rst stageoutput impedance,

l1. In combination with a low impedance source and a low impedance load,a two-stage arnpliner adapted to be connected in cascade betweensaidsource and said load which comprises a nrst transistor amplifier stageof the groundedbase conguration having an intrinsically low inputimpedance and an intrinsically high output impedance, wherein the inputimpedance of saidstage is matched to that of the source by selection ofthe magnitude of a rst stage loading resistance R21 and having outputterminals, and a second transistor amplifier stage of thegrounded-collector conguration having an intrinsically high inputimpedance Rin2 and an in trinsically low output impedance, thetransistor of vsaidsrecond stage being characterized by a ratio ofshortcircuit collect current increments to emitter current incrementswhich exceeds unity, an input circuit interconnecting the base electrodeoi the second stage transistor with its collector electrode andconnected to the rst stage output terminals', an out-put circuitinterconnecting the emitter electrode of second stage transistor withits collector electrode, said low impedance load and a second stageloading resistor R22 being connected in said output circuit, said secondstage loading resistor being proporwhere rc2-:emitter resistance of thesecond stage transistor rb.: :base resistance of the second stagetransistor rcgzcollector resistance of the second stage tran sistor rm2:mutual resistance of the second stage transistor Rie2=input resistanceof the second transistor l stage,

whereby the second stage input impedance is matched with the rst stageoutput impedance.

HAROLD L. BARNEY.

No references cited.

